The uncertainty relation for an assembly of Planck-type oscillators. A possible GR-quantum mechanics connection

Agop, M.; Griga, V.; Ciobanu, Brânduşa; Buzea, Cristina; Stan, Cristina; Tatomir, Dorian

doi:10.1016/s0960-0779(96)00101-4

Cited by 10 publications

(9 citation statements)

References 8 publications

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“…The Lie algebra associated to the group (24) is If H has energy significance, then condition (30) shows that a representative point from space ( x, y ) (which is in motion on a surface of constant energy (22)), can be also found on a surface of constant probabilistic density (ergodic condition) in Stoler's sense [33]:…”

Section: Shannon's Informational Entropy and Transitivity Manifoldsmentioning

confidence: 99%

“…When taking into consideration, for the group (45), the parameterization from [23], the following infinitesimal generators of the above-mentioned group will be obtained] [63]: Once we fulfill the conditions of the theorem [38], the invariant functions can be found, simultaneously to the actions of the groups (5) and 46 where μ and ν are expressed as (see [63]):…”

Section: Quantum Mechanics and Informational Energy -Generalized Uncementioning

confidence: 99%

“…where φ is the value of k, assumed fixed. The square value of Q represents the value of the constant from (30), which determines the transitivity manifolds of the group (1) (see [63]).…”

Section: Quantum Mechanics and Informational Energy -Generalized Uncementioning

confidence: 99%

See 2 more Smart Citations

Implications of Quantum Informational Entropy in Some Fundamental Physical and Biophysical Models

Agop¹,

Gavriluţ²,

Buzea³

et al. 2015

Selected Topics in Applications of Quantum Mechanics

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Correspondingly, the theoretical models that describe the complex systems dynamics become more and more advanced [ -]. For all that, this problem can be solved by taking into account that the complexity of the interaction process implies various temporal resolution scales, and the pattern evolution implies different degrees of freedom [ ].[In order to develop new theoretical models we must state the fact that the complex systems displaying chaotic behavior are recognized to acquire self-similarity space-time structures can appear in association with strong fluctuations at all possible space-time scales [ -]. "fterwards, for temporal scales that are large with respect to the inverse of the highest Lyapunov exponent, the deterministic trajectories are replaced by a set of potential trajectories and the concept of definite positions by that of probability density] [ ]. "n interesting example is the collisions processes in complex systems, where the dynamics of the particles can be described by non-differentiable curves.Since non-differentiability can be considered a universal property of complex systems, it is mandatory to develop a non-differentiable physics. In this way, by considering that the complexity of the interaction processes is replaced by non-differentiability, using the entire range of quantities from the standard physics differentiable physics is no longer required [ ].This topic was developed in the Scale Relativity Theory SRT [ , ] and in the non-standard Scale Relativity Theory NSSRT [ -]. [In the framework of SRT or NSSRT we assume that the movements of complex system entities take place on continuous but non-differentiable curves fractal curves so that all physical phenomena involved in the dynamics depend not only on the space-time coordinates but also on the space-time scales resolution. In this conjecture, the physical quantities that describe the dynamics of complex systems can be considered as fractal functions. In addition, the entities of the complex system may be reduced to and identified with their own trajectories. In this way, the complex system's behavior will be identical to the one of a special interaction-less fluid by means of its geodesics in a nondifferentiable fractal space] [ , , ].In such context notions as informational entropy, Onicescu informational energy etc become important in the Nature description. These notions will be correlated with the fractal part of the physical quantities that describe the dynamics of complex systems. . Informational entropy and energyIndependently of scale resolution, the motion, either on infragalactic scale for instance, the planetary motion , or on atomic scale for instance, the motion of the electron around its nucleus takes place on conics ellipses . Such motion in invariant with respect to the SL R group. In what follows, we shall consider this invariance only with respect to the motion on atomic scale. . . SL R invariance and canonic formalismSL R group is the group of transformations [ -]

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Section: Shannon's Informational Entropy and Transitivity Manifoldsmentioning

confidence: 99%

Section: Quantum Mechanics and Informational Energy -Generalized Uncementioning

confidence: 99%

See 1 more Smart Citation

Implications of Quantum Informational Entropy in Some Fundamental Physical and Biophysical Models

Agop¹,

Gavriluţ²,

Buzea³

et al. 2015

Selected Topics in Applications of Quantum Mechanics

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show abstract

“…)−1 S Q ) can be identified, without a constant factor, with the informational non-differentiable entropy (defined by analogy with the Shannon informational entropy [26][27][28][29][30][31]):…”

Section: Informational Non-differentiable Entropymentioning

confidence: 99%

Informational Non-Differentiable Entropy and Uncertainty Relations in Complex Systems

Agop

Gavriluţ

Crumpei³

et al. 2014

Entropy

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Considering that the movements of complex system entities take place on continuous, but non-differentiable, curves, concepts, like non-differentiable entropy, informational non-differentiable entropy and informational non-differentiable energy, are introduced.First of all, the dynamics equations of the complex system entities (Schrödinger-type or fractal hydrodynamic-type) are obtained. The last one gives a specific fractal potential, which generates uncertainty relations through non-differentiable entropy. Next, the correlation between informational non-differentiable entropy and informational non-differentiable energy implies specific uncertainty relations through a maximization principle of the informational non-differentiable entropy and for a constant value of the informational non-differentiable energy. Finally, for a harmonic oscillator, the constant value of the informational non-differentiable energy is equivalent to a quantification condition. Keywords:non-differentiable entropy; informational non-differentiable entropy; informational non-differentiable energy; uncertainty relations Entropy 2014, 16 6043

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“…It is obtained by a growing process along a direction (anisotropy direction) starting with a thermal breather. It develops through a generalized coherence (amplitude and phase correlation, 15,16) ) generating, in the primary stages, the thermal breather pair, and in the final ones, the thermal cluster. In such a context, the SL interface anisotropy is induced by the fractal of growth as an intrinsic property of it (see Appendix C).…”

Section: Fractal Dimension Dynamics Of the Solidification Processmentioning

confidence: 99%

Fractal Characteristics of the Solidification Process

et al. 2004

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Assimilating the solid-liquid interface to a binary domain described by a set of coupled equations, one studies the solidification process. The numerical solutions of the thermal breather, the thermal breather pair and the thermal cluster type are associated to a virtual crystallization germ, a stable crystallization germ and a crystalline grain, respectively. The fractal characteristics of the solidification process are analyzed by means of fractal dimension dynamics.

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The uncertainty relation for an assembly of Planck-type oscillators. A possible GR-quantum mechanics connection

Cited by 10 publications

References 8 publications

Implications of Quantum Informational Entropy in Some Fundamental Physical and Biophysical Models

Implications of Quantum Informational Entropy in Some Fundamental Physical and Biophysical Models

Informational Non-Differentiable Entropy and Uncertainty Relations in Complex Systems

Fractal Characteristics of the Solidification Process

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